Question

2) Find two bases for the row space of A: a. One that consists of rows of A b. One that is not a subset of the rows of A (i.e. the basis vectors are not rows of A). Г1 020 0 1-2 0 3 00 015 Note: RREF(A)- and RREF(A) 0 0 0 1

Answer 1

2). It is apparent from the RREF of A^T, that its 3 columns i.e. the 1^st, 2^nd and 4^th columns of A^T are linearly independent and its 3^rd column is a linear combination of its first 2 columns. Therefore, 3 rows of A are linearly independent and since the 4^th row of A is a zero row, hence the first 3 rows of A are linearly independent.

Hence the 2 bases of the row space of A are the sets { (1,0,1,0,1),(0,1,-2,0,3),(0,0,0,1,-5)} and {(1,0,0,0,0),(0,1,0,0,0),(0,0,1,0,0)}.